Q120 / 160 · TS EAMCET 2024 (11 May Shift 1) · Mathematics

The general solution of the differential equation $\left(6 x^2-2 x y-18 x+3 y\right) d x-\left(x^2-3 x\right) d y=0$ is

  • Correct answer
    A
    $2 x^3-x^2 y-9 x^2+3 x y+c=0$
  • B
    $4 x^3-2 x^2 y-6 x^2+6 x y+c=0$
  • C
    $2 x^3-4 x y-y^2-x+3 y+c=0$
  • D
    $3 x^2+5 x y-2 y^2-4 x-2 y+c=0$

Solution

$\begin{aligned} & 6 x^2 d x-18 x d x+3 y d x+3 x d y-2 x y d x-x^2 d y=0 \\ \Rightarrow & 2 d\left(x^3\right)-9 d\left(x^2\right)+3 d(x y)-d\left(x^2 y\right)=0 \\ \Rightarrow & 2 x^3-9 x^2+3 x y-x^2 y+c=0\end{aligned}$

Hence, the correct answer is option: 'A'.

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